> We propose the Probabilistic Sentential Decision Diagram (PSDD): A complete and canonical representation of probability distributions defined over the models of a given propositional theory. Each parameter of a PSDD can be viewed as the (conditional) probability of making a decision in a corresponding Sentential Decision Diagram (SDD). The SDD itself is a recently proposed complete and canonical representation of propositional theories. We explore a number of interesting properties of PSDDs, including the independencies that underlie them. We show that the PSDD is a tractable representation. We further show how the parameters of a PSDD can be efficiently estimated, in closed form, from complete data. We empirically evaluate the quality of PSDDs learned from data, when we have knowledge, a priori, of the domain logical constraints.
Still working on my understanding but Professor Darwiche gave a lecture on the material in one of my classes. Salient bit:
> The problem we tackle here is that of developing a representation of probability distributions in the presence of massive, logical constraints. That is, given a propositional logic theory which represents domain constraints, our goal is to develop a representation that induces a unique probability distribution over the models of the given theory.
http://reasoning.cs.ucla.edu/fetch.php?id=136&type=pdf
Abstract:
> We propose the Probabilistic Sentential Decision Diagram (PSDD): A complete and canonical representation of probability distributions defined over the models of a given propositional theory. Each parameter of a PSDD can be viewed as the (conditional) probability of making a decision in a corresponding Sentential Decision Diagram (SDD). The SDD itself is a recently proposed complete and canonical representation of propositional theories. We explore a number of interesting properties of PSDDs, including the independencies that underlie them. We show that the PSDD is a tractable representation. We further show how the parameters of a PSDD can be efficiently estimated, in closed form, from complete data. We empirically evaluate the quality of PSDDs learned from data, when we have knowledge, a priori, of the domain logical constraints.
Still working on my understanding but Professor Darwiche gave a lecture on the material in one of my classes. Salient bit:
> The problem we tackle here is that of developing a representation of probability distributions in the presence of massive, logical constraints. That is, given a propositional logic theory which represents domain constraints, our goal is to develop a representation that induces a unique probability distribution over the models of the given theory.